REVERE, Mass. Where else but in Massachusetts would a Republican senator, facing a tight election, want to focus on how much he agrees with the Democratic president?

“I’m the second-most bipartisan senator in the United States Senate,” Sen. Scott Brown said last week while meeting with military veterans in Revere. “I vote with my party about 54 percent of the time.”

That’s what a Congressional Quarterly study of Scott Brown’s 2011 votes found. And Brown makes sure to stress his bipartisan record every chance he gets.

Brown told the veterans and their families he found himself agreeing with the president on allowing people to refinance their mortgages if they owe more than what their houses are worth. He also found common ground with the president on making it illegal for members of Congress to trade stocks based on privileged information.

Brown’s campaign manager pointed out that when the president has an opinion on a Senate vote, Brown sides with him 70 percent of the time. Brown understands that this is a winning strategy for a Republican in Massachusetts.

“The fact that you have Sen. [John] Kerry down there and Sen. Brown down there is no different than Sen. Brooke and Sen. Kennedy,” Brown said, referring to former Sen. Ed Brooke, a Republican, and the late Sen. Edward Kennedy. “People like that balance. It works.”

“We do have a tradition in this state of liberal or moderate Republicans going back to Ed Brooke,” said Alan Wolfe, a professor of political science at Boston College. “So there is a niche for Scott Brown to occupy.”

Whether it’s by nature or political savvy or both, Brown’s ability to be “Mr. Moderate” in the Senate is working for him. Most polls show him ahead of his likely Democratic rival, Harvard law professor Elizabeth Warren. The most recent survey from Western New England University finds Brown ahead among independents, among people under 50, among people 65 and over, and in central and western Massachusetts.

In a conference call with reporters Monday, John Walsh, the chairman of the Massachusetts Democratic Party, conceded that Brown is a tough opponent.

“I expect if the election were held today Scott Brown would win,” Walsh said. “I think this is an election that’s going to be fought and close right down to the end because Scott Brown is a smart politician. You see him strategically slicing thin slices of the electorate, trying to find wedge issues to cobble together a majority win.”

Brown and Warren recently tussled over one wedge issue: whether employers should have the right to withhold health coverage for certain services, such as contraception, if they object for religious or moral reasons.

But Brown is also raising other issues. At the veterans meeting, he talked about his opposition to Pentagon plans to raise premiums for retirees enrolled in Tricare, the health care program for service members.

“Now they’re going to be raising the premiums,” Brown said. “They’re going to be eventually, I think, trying to cut Tricare altogether and morph you into Medicare or some other program.”

Brown’s message is not just that he’s in the middle of the road, he points out that his ability to work across party lines gets things done. He mentioned another bill he cosponsored that has become law that provides employer tax credits if they hire National Guard members.

“I’m not going to be the social crusader like Professor Warren,” Brown said. “I’m going to be the jobs crusader.”

That pragmatism comes through when asked how he views the atmosphere in Congress that has driven his fellow New England moderate Republican, Olympia Snowe, to retire.

“I’ve been disgusted by a lot of what’s been going on, but I’m going to continue to be part of the solution,” Brown said. “I’m a problem solver. I’m not a rock thrower.”

Brown tells the veterans how he got the president to help him with his bill banning insider trading by members of Congress. The State of the Union speech had just ended when Brown approached President Obama.

“So meanwhile that whole row cleared out and, therefore, I actually get to walk up right next to the aisle as the president’s coming up, and I’m saying to myself, ‘Man! He wants an insider trading bill. I have one,’ ” Brown explained. “So I said, ‘Mr. President, my insider trading bill is on Harry Reid’s desk. Tell him to get it out.’ And he looked right at me and he says, ‘I will. I’ll tell him to get it out.’ Problem was he was miked up live with Fox.”

So, Brown says, the president got his bill to the Senate floor, where it passed.